Nuprl Lemma : r2-det_functionality
∀[p,q,r,p',q',r':ℝ^2]. (|pqr| = |p'q'r'|) supposing (req-vec(2;r;r') and req-vec(2;q;q') and req-vec(2;p;p'))
Proof
Definitions occuring in Statement :
r2-det: |pqr|,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
req: x = y,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
req-vec: req-vec(n;x;y),
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
r2-det: |pqr|,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
true: True,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
r2-det_wf,
req-vec_wf,
false_wf,
le_wf,
real-vec_wf,
rsub_wf,
radd_wf,
rmul_wf,
lelt_wf,
req_weakening,
req_functionality,
rsub_functionality,
radd_functionality,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
dependent_functionElimination,
productElimination
Latex:
\mforall{}[p,q,r,p',q',r':\mBbbR{}\^{}2].
(|pqr| = |p'q'r'|) supposing (req-vec(2;r;r') and req-vec(2;q;q') and req-vec(2;p;p'))
Date html generated:
2017_10_03-AM-11_41_23
Last ObjectModification:
2017_04_11-PM-05_29_29
Theory : reals
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